Optimal penalty parameters for symmetric discontinuous Galerkin discretisations of the time-harmonic Maxwell equations

D. Sarmany, F. Izsak, Jacobus J.W. van der Vegt

Research output: Book/ReportReportProfessional

30 Citations (Scopus)

Abstract

We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are $i)$ valid in the pre-asymptotic regime; $ii)$ solely depend on the geometry and the polynomial order; and $iii)$ are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order ($p = 1, 2, 3, 4$) hierarchic $H(\mathrm{curl})$-conforming polynomial basis functions.
Original language Undefined Enschede University of Twente, Department of Applied Mathematics 34 Published - Jan 2010

Publication series

Name Memorandum / Department of Applied Mathematics Department of Applied Mathematics, University of Twente 1914 1874-4850 1874-4850

Keywords

• METIS-270717
• Numerical mathematics
• EWI-17325
• Electromagnetic waves
• MSC-00A72
• Scientific computation
• Finite Element Method
• IR-69763